“…The guiding example is when m = 1. In that case the WZW equation is the much studied complex Monge-Ampère equation; it is known that V is not smooth in general (see [Darvas 2014;Darvas and Lempert 2012;Lempert and Vivas 2013]), and C 1,1 is the best one can hope for (see [Błocki 2012;Chen 2000;Chu et al 2017]).…”
We prove that the solution of a Wess-Zumino-Witten type equation from a domain D in ރ m to the space of Kähler potentials can be approximated uniformly by Hermitian-Yang-Mills metrics on certain vector bundles. The key is a new version of Berndtsson's theorem on the positivity of direct image bundles.
“…The guiding example is when m = 1. In that case the WZW equation is the much studied complex Monge-Ampère equation; it is known that V is not smooth in general (see [Darvas 2014;Darvas and Lempert 2012;Lempert and Vivas 2013]), and C 1,1 is the best one can hope for (see [Błocki 2012;Chen 2000;Chu et al 2017]).…”
We prove that the solution of a Wess-Zumino-Witten type equation from a domain D in ރ m to the space of Kähler potentials can be approximated uniformly by Hermitian-Yang-Mills metrics on certain vector bundles. The key is a new version of Berndtsson's theorem on the positivity of direct image bundles.
“…The guiding example is when m = 1. In that case the WZW equation is the much studied complex Monge-Ampère equation; it is known that V is not smooth in general (see ; Darvas and Lempert 2012; Lempert and Vivas 2013]), and C 1,1 is the best one can hope for (see Chen 2000;Chu et al 2017]).…”
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